Question

1. A car travels from stop A to stop B with a speed of 30 km/h and then returns back to A with a speed of 50 km/h. Find
(i) displacement of the car.
(ii) distance travelled by the car.
(iii) average speed of the car.

Answer 1

• Given

• A car travels from stop A to stop B with speed = 30 km/h
• It returns back to stop A with speed = 50 km/h

• To find

• (i) displacement of the car.
• (ii) distance travelled by the car.
• (iii) average speed of the car.

• Solution

(I) displacement of the car.

• Displacement = 0

Explanation : Displacement will be zero because Car travels from stop A and then returns to stop B. And the car has travelled some distance but its displacement will be zero because it returned back to the point from where it started.

Displacement :- It is the shortest distance between the initial and the final position.

(II) distance travelled by the car.

• Distance = 2x

Explanation :

Let the distance from stop A to stop B be x.

The car travels from stop A to B and then returns back to A.

•°• Distance = x + x = 2x

(III)

Average speed of the car.

As we know,

• Time = Distance/Speed

⇛ x/50 + x/30

⇛ 8x/150

• Time = 8x/150

As we know,

• Avg. speed = Total distance travelled/Total time taken

⇛ 2x/8x/150

⇛ (2x × 150) × 8x

⇛ 37.5 km/h

• Avg. Speed = 37.5 km/h

Answer 2

Given:-

→ Speed of the car, when it travels from

stop A to stop B = 30 km/h

→ Speed of the car, when it returns back

from stop B to stop A = 50km/h

To find:-

→ Displacement of the car .

→ Distance travelled by the car .

→ Average speed of the car .

Solution:-

As per as the question, the car travels from stop A to stop B and again returns from stop B to stop A.

Since, the initial and final points of the car are same. Thus, displacement of the car is zero.

Also from the question, we can understand that distance travelled by the car in both cases is same. Let the distance travelled from A to B be 'd' km. Thus total distance travelled :-

= d + d

= 2d km

Time = Distance/Speed

Time taken to travel from A to B :-

= d/30 h

Time taken to travel from B to A :-

= d/50 h

Average speed :-

= Total distance/Total time

=> Vₐᵥ = [d + d]/[d/30 + d/50]

=> Vₐᵥ = [2d]/[5d + 3d/150]

=> Vₐᵥ = 2d/[8d/150]

=> Vₐᵥ = 2d×150/8d

=> Vₐᵥ = 150/4

=> Vₐᵥ = 37.5 km/h

[Note : In this case, we can also calculate average speed of the car by using the direct formula :-

=> Vₐᵥ = 2v₁v₂/v₁ + v₂ ]

Thus:-

• Displacement of the car is zero.

• Distance travelled by the car is 2d.

• Average speed of the car is 37.5km/h.